The area bounded by the coordinate axes and normal to the curve y=logex at the point P (1, 0), is

We have,

$y = \log_{e} x \Rightarrow \frac{d y}{d x} = \frac{1}{x} \Rightarrow {(\frac{d y}{d x})}_{p} = 1$

The equation of the normal at (1, 0) is

$y - 0 = - 1 (x - 1) \Rightarrow x + y = 1$

Clearly, it makes a triangle of area $\frac{1}{2}$ sq. unit with the

coordinate axes.

The area bounded by the coordinate axes and normal to the curve $y = \log_{e} x$ at the point $P (1, 0)$ , is